Low total excursion dispersion maps

ABSTRACT

A process optically transports digital data over an all-optical long-haul communication path. The process includes transporting digital optical data signals at a selected bit rate and a selected wavelength over a sequence of transmission spans. The sequence includes 70 percent or more of the spans of the long-haul all-optical communication path. Each span of the sequence has a primary local maximum optical power point for the wavelength on a transmission fiber and nearest to an input of the span. The transporting causes a cumulative dispersion of each signal to evolve such that residual dispersions per span are positive over some of the spans and are negative over other of the spans. At the primary local maximum power points, magnitudes of cumulative dispersions of the signals in pico seconds per nanometer remain at less than 32,000 times the inverse of the bit rate in giga bits per second.

This is a continuation-in-part application of application Ser. No.10/442,287, filed May 20, 2003.

BACKGROUND

1. Field of the Invention

The invention relates to optical communication systems and processes.

2. Discussion of the Related Art

In optical communications systems, transmission optical fibers causechromatic dispersion and nonlinear optical effects. Both effects degradeoptical pulses in ways that increase transmission errors. To reduce thepulse degradation caused by chromatic dispersion, optical communicationsystems typically incorporate dispersion compensation devices, e.g.,dispersion compensating fibers (DCFs), dispersion compensatinginterferometers, or dispersion compensating grating systems, tocompensate for chromatic dispersion. To reduce the pulse degradationcaused by nonlinear optical effects, long-haul optical communicationsystems typically manage dispersion through special processes andspecial dispersion maps.

The special processes involve transmitting optical pulses overtransmission spans in a pseudo-linear transmission regime (PLTR). ThePLTR is defined by the following operating conditions: a bit rate of 10Giga bits per second (Gb/s) or higher, a wavelength of 1.25 micrometers(μm) to 1.7 μm, a pulse full width at half maximum power of 60 ps orless, and a pulse duty cycle of between 10% and 70%. The transmissionspans are typically single mode optical fibers with high magnitude ofthe dispersions that are about +2 pico seconds (ps) or more pernanometer (nm) per kilometer (km) at communication wavelengths. Due tothis high dispersion, the transmission spans cause substantialbroadening of optical pulses. In the PLTR, this pulse broadening causesmultiple optical pulses from nearby frequency channels to substantiallyoverlap in time, which averages inter-pulse interactions and reducespulse distortion from inter-channel interactions.

The special dispersion maps result from chromatic dispersioncompensation devices that are located at the input and/or output ends oftransmission spans. Herein, a dispersion map plots the cumulativedispersion as a function of transmission distance along an opticalcommunication path. The dispersion compensation devices at the inputand/or output ends of transmission spans produce abrupt changes incumulative dispersion along the communication path thereby producingnontrivial dispersion maps.

FIG. 1 shows a dispersion map 8 of an optical communication path witheight identical transmission spans. Each transmission span includes 100km of positive dispersion single mode fiber (SMF) 10. Between the endsof the SMFs 10 of adjacent transmission spans is a DCF 12. Along eachtransmission SMF 10, the cumulative dispersion increases linearly withdistance. Along each DCF 12, the cumulative dispersion decreaseslinearly with distance. The lengths of the DCFs 12 are selected toproduce full compensation of the dispersion 14 that accumulated on thepreceding transmission SMF 10. This full compensation of chromaticdispersion produces a dispersion map in which the cumulative dispersionis periodic in a span-by-span manner. This dispersion map is referred toas a full-span compensation map.

While full-span compensation maps do compensate very well for the pulsedegradation caused by chromatic dispersion, these maps do not completelycorrect for the pulse degradation caused by nonlinear optical effects.In particular, the span-by-span periodicity suggests that any residualpulse degradation from nonlinear optical effects will add constructivelywith the number of spans as a pulse travels along the opticalcommunication path. In long haul communication systems, thisconstructive accumulation of nonlinear distortions can be the primarycontribution to the bit error rate (BER) and pulse degradation:

FIG. 2 shows a dispersion map 16 for an optical communication systemthat includes a series of identical transmission spans of positivedispersion SMF, a DCF located after each transmission span, apre-transmission dispersion compensator, and a post-transmissiondispersion compensator. The dispersion map 16 provides pre-transmissiondispersion compensation, C_(PRE), prior to the first span, in-linedispersion compensation, C_(IL), after each transmission span, andpost-transmission dispersion compensation, C_(POST), after the lasttransmission span. In the dispersion map 16, the in-line dispersioncompensation, C_(IL), does not entirely compensate for the positivedispersion that accumulates in the preceding transmission span ofpositive dispersion SMF. Instead, a residual dispersion per span,C_(RDPS), remains after the in-line dispersion compensation for eachspan. A nonzero and constant value of C_(RDPS), as e.g., in the map 16,produces a dispersion map that is referred to as a singly periodic map.If the value of C_(RDPS) is the same and zero for each span as, e.g., inFIG. 1, the dispersion map is referred to as a full-span compensationmap.

Some special dispersion maps better compensate for the pulse degradationcaused by nonlinear optical effects. In particular, it is believed thatoptimal values of C_(PRE) exist for singly periodic dispersion maps thatare EDFA pumped. For such maps, the approximately optimal C_(PRE) isbelieved to satisfy:C _(PRE)=−NC_(RDPS)/2+(D/α)ln([1−exp(−αL _(span))]/2)Here, α is the power loss per unit length in a transmission span, N isthe total number of spans, D is the dispersion in optical fibers of thetransmission spans, and L_(span) is the length of each span. The aboveequation defines C_(PRE) in terms of C_(RDPS) when the physicalparameters of the transmission spans, i.e., L_(span), D, and α, aregiven. A singly periodic map that satisfies the above optimizationequation will compensate well for the effects of intra-channelcross-phase modulation and intra-channel four-wave mixing.

Among dispersion maps that satisfy the above optimization equation,singly periodic maps with small CRDPs's seem to produce large amounts oftiming jitter in transmitted optical pulses. Normally, large amounts oftiming jitter are not desirable, because timing jitter can causereception errors.

Various nontrivial dispersion maps are described in U.S. Pat. No.6,583,907 issued Jun. 24, 2003; U.S. Pat. No. 6,606,176 issued Aug. 12,1999; and U.S. patent application Ser. No. 10/152,645, filed May 21,2002 by R.-J. Essiambre et al all of which are incorporated herein byreference in their entirety. While special dispersion maps have reducedthe amount of pulse degradation from nonlinear optical effects,processes for further reducing such pulse degradation are desirable.Such processes could enable higher bit rates and/or higher power levelsthat allow optical transmission of data over longer distances.

BRIEF SUMMARY

The various embodiments relate to long-haul all-optical transmissionsystems and processes that produce low total excursion. These mapsreduce pulse degradation from nonlinear optical effects whentransmission is performed in the pseudo-linear transmission regime(PLTR) over long haul distances. The new optical transmission systemsand processes open potentials for optically transmitting data at higherbit rates and/or higher power levels that enable optical transmission ofdata over longer distances.

In one aspect, a process optically transports digital data over along-haul all-optical communication path. The process includestransporting digital optical data signals, e.g., optical pulses, at aselected bit rate and wavelength over a consecutive or non-consecutivesequence of transmission spans. The sequence includes 70 percent or moreof the spans of the long-haul all-optical communication path. Each spanof the sequence is configured to have one or more local maximum opticalpower points for the selected wavelength on a transmission fiberthereof. The transporting step causes a cumulative dispersion of eachtransported digital optical data signal to evolve along a dispersion mapof the path. The map is such that residual dispersions per span oversome ones of the spans are positive at the selected wavelength and overother ones of the spans are negative at the selected wavelength. Foreach span, a primary local maximum power point at the selectedwavelength is the local maximum power point located nearest to a signalinput in the associated fiber. At the primary local maximum power pointof each span of the sequence, magnitudes of cumulative dispersions ofthe optical data signals in pico seconds per nanometer are less than32,000 times the inverse of the bit rate in giga bits per second.

In some embodiments, cumulative dispersions of the digital optical datasignals in pico seconds per nanometer at the primary local maximum powerpoint of each span of the sequence are less than about 16,000 times theinverse of the bit rate in giga bits per second. In some embodiments,each transmission fiber is a non-hybrid transmission optical fiber andeach transmission span of the sequence includes a dispersion compensatorcascaded with the transmission fiber of the same span.

In some embodiments, the transporting may include transporting digitaloptical data signals or pulses in a pseudo-linear transmission regime(PLTR).

The dispersion map may be doubly periodic or have a non-definiteperiodicity.

In embodiments where the map is doubly periodic, the process may furtherinclude pre-transmission dispersion compensating each digital opticaldata signal with a precompensation C_(PRE) whereC_(PRE)=−NC_(RDPS)/2+(D/α)ln([1−exp(−αL_(span))]/2)±300 ps/nm. Here, αand D are the respective average power loss per unit length in thetransmission fibers and the average dispersion in the transmissionfibers. Here, C_(RDPS) is the average of the residual dispersions perspan over the transmission spans of the path, and L_(span) is theaverage length of said transmission fibers. N is the number oftransmission spans in a repeat unit of the doubly periodic map, i.e., arepeat period of the map that is greater than one span and less than theentire path.

In another aspect, a long-haul all-optical communication system fortransmitting digital optical data signals, e.g., optical pulses, at aselected bit rate and a selected wavelength includes a consecutive ornon-consecutive sequence of optical transmission spans. The spans of thesequence form at least 70 percent of the spans of the long-haulall-optical communication path. Each span of the sequence has in thepath a transmission single-mode optical fiber, an optical amplifier, anda dispersion compensator. The path causes cumulative dispersions ofdigital optical data signals to evolve over a dispersion map such thatresidual dispersions per span are positive over some of the spans forthe selected wavelength and are negative over others of the spans forthe selected wavelength. The path is configured to produce one or morelocal maximum optical power points in each transmission optical fiber.For the selected wavelength, the local maximum power point nearest tothe signal input of one of the fibers is the primary local maximum powerpoint of the associated span. The path is configured such that at theprimary local maximum power points of the spans in the sequence,magnitudes of cumulative dispersions of the digital optical data signalsin pico seconds per nanometer are less than 32,000 times the inverse ofthe bit rate in giga bits per second.

In some embodiments, the dispersion map is a doubly periodic map or is amap having a non-definite periodicity. The combined length of thetransmission fibers may be 2,000 kilometers or more.

In some embodiments, each transmission fiber is a non-hybridtransmission optical fiber.

In some embodiments, the transmitter is configured to transmit opticalpulses in a pseudo-linear transmission regime.

In another aspect, a long-haul optical communication system transmitsoptical pulses at a selected bit rate and a selected wavelength. Thesystem includes a consecutive or non-consecutive sequence of spansforming 80 percent of the transmission spans of the all-opticallong-haul optical communication path. Each span of the sequence includesa positive dispersion transmission optical fiber, an optical amplifier,and a dispersion compensator. The path is configured to cause cumulativedispersions of the pulses to evolve such that residual dispersions perspan are positive over some ones of the spans of the consecutive ornon-consecutive sequence and are negative over other ones of the spansof the sequence. The path is configured to produce in each fiber one ormore local maximum optical power points at the selected wavelength. Eachfiber has one or more segments where during operation a time-averagedoptical power at the selected wavelength is at least 0.2 times thelargest value along the same fiber of the time-averaged optical power atthe selected wavelength. A primary one of the segments is such that anintegral of a time-averaged optical power at the selected wavelengthalong the length of the primary one of the segments is greater than orequal to an integral of the optical power at the selected wavelengthalong the length of any other one of the segments for the same fiber.The path is such that in said primary ones of the segments of thefibers, magnitudes of cumulative dispersions of the optical pulses inpico seconds per nanometer are less than 32,000 times the inverse of thebit rate in giga bits per second.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a conventional full-span compensation dispersion map inwhich the residual dispersion per span is zero;

FIG. 2 shows a conventional singly periodic dispersion map in which theresidual dispersion per span is nonzero and constant over the opticalcommunication path;

FIG. 3A shows an optical communication path;

FIG. 3B is a flow chart illustrating a process for operating the opticalcommunication path of FIG. 3A;

FIG. 3C illustrates power evolution of an optical signal as the signalpropagates along a transmission span of single-mode optical fiber in anembodiment that relies on erbium doped fiber (EDF) amplification;

FIG. 3D illustrates power evolution of an optical signal as the signalpropagates along a transmission span of single-mode optical fiber in anembodiment that relies on backwards Raman amplification;

FIG. 3E illustrates power evolution of an optical signal as the signalpropagates along a transmission span of single-mode optical fiber in anembodiment that relies on combined forward and backwards Ramanamplification;

FIG. 4 shows an in-line amplifier of the optical communication path ofFIG. 3A;

FIGS. 5A plots predictions for the required optical signal to noiseratios (ROSNRs) needed for a bit error rate of 10⁻⁹ during singlechannel operation of an optical communication path with a singlyperiodic dispersion map;

FIGS. 5B plots predictions for the ROSNRs needed for a bit error rate of10⁻⁹ during dense wavelength division multiplexed (DWDM) operation of anoptical communication path with a singly periodic dispersion map;

FIG. 6 shows a low total excursion, singly periodic dispersion map thatmay be incorporated into the optical communication path of FIG. 3;

FIG. 7 shows a low total excursion, doubly periodic dispersion map thatis incorporated into some embodiments of the optical communication pathof FIG. 3;

FIG. 8 shows a low total excursion, dispersion map of non-definiteperiodicity that is incorporated into some embodiments of the opticalcommunication path of FIG. 3;

FIG. 9 illustrate eye closure penalties for optical communication pathsaccording to FIG. 3 for a singly periodic dispersion map; and

FIG. 10 illustrates eye closure penalties for an embodiment of theoptical communication path of FIG. 3, which has a doubly periodicdispersion map.

In the Figures and text, like reference numerals indicate elements withsimilar functions.

DETAILED DESCRIPTION

Herein, a long haul, all-optical communication path includes a series oftransmission spans whose combined length is more than about 1,000kilometers. In such a path, the series of transmission spans may be2,000 kilometers long or longer.

FIG. 3A shows a long haul, all-optical, communication path 20 thatconnects an optical transmitter 22, which encodes digital data into astream of digital optical data signals, to an optical receiver 24, whichextracts digital data from such streams of digital optical data signals.The stream of digital data may encode the data as a stream of opticalpulses or as a stream of phase modulations on an optical carrier and mayencode the data in an optical return-to-zero (RZ) format or an opticalnon-return-to-zero (NRZ) format. The optical communication path 20includes the optical transmission spans 26 and in-line opticalamplifiers 28, which are disposed between adjacent pairs of the opticaltransmission spans 26. Each optical transmission span 26 includes asingle mode, optical fiber (SMF) for transmitting optical signals. Thetransmission SMFs are typically non-hybrid single mode optical fiberswith dispersions whose magnitudes are at least 2 ps per nm per km. Thedispersion is substantially constant along a transmission fiber'slength. In embodiments described below, the transmission spans 26 usepositive dispersion SMFs (PDSMFs) as transmission fibers, butembodiments where the transmission spans 26 use negative dispersion SMFs(NDSMFs) are also in the scope of the invention. Exemplary transmissionPDSMFs include standard single mode optical fibers, dispersion shiftedsingle mode optical fibers, and various single mode optical fibersavailable under the TrueWave® product names from OFS Corporation ofNorcross, Ga. USA and Copenhagen, Denmark. Typically, each transmissionSMF is 50 km or more long, preferably is about 80 km or longer, and morepreferably is between 80 km and 120 km long. Each in-line opticalamplifier 28 is a lumped device that produces both optical amplificationand in-line dispersion compensation.

FIG. 4 shows one in-line optical amplifier 28 of the long haulall-optical communication path 20 of FIG. 3A. The in-line opticalamplifier 28 includes optical amplifier stages 36, 37; a DCF 38; andother optical components 40. Exemplary optical amplifier stages 36, 37include rare earth doped amplifiers, e.g., erbium doped fiber amplifiers(EDFAs), and/or Raman amplifiers. For embodiments where the transmissionspans 26 are PDSMFs, the DCF 38 is a single-mode optical fiber, whichhas a negative dispersion. For spans 26 of PDSMF, exemplary DCFs 38 havedispersions of about −85 ps/nm. For embodiments where the transmissionspans 26 are NDSMFs, the DCFs 38 have positive dispersions. In exemplaryin-line optical amplifiers 28, the amplifier stage 37 is often designedso that the DCF 38 operates at a much lower power than high powerportions of the transmission spans 26. For that reason, nonlinearoptical effects are often negligible in the DCF 38. Exemplary opticalcomponents 40 include optical add/drop devices, optical multiplexers,optical demultiplexers, etc.

The optical communication path 20 incorporates pre-transmission,post-transmission, and in-line dispersion compensation to producedispersion mapping. The pre-transmission dispersion compensation,C_(PRE), is produced by a dispersion compensator 32, e.g., a DCF,located before the optical amplifier 30 of the transmitter 22. Thenegative or positive post-transmission dispersion compensation,C_(POST), is produced by a dispersion compensator 34, e.g., a DCF or asection of standard SMF depending on the sign of C_(POST). Thedispersion compensator 34 is located between the last in-line opticalamplifier 28 of the optical communication path 20 and the opticalreceiver 24. The in-line dispersion compensation, C_(IL), is produced bythe DCFs 38 that are located in the in-line amplifiers 28. In thelong-haul all-optical communication optical path 20, the configurationof the dispersion compensators 32, 38, 34 can produce dispersion maps ofthe types shown in FIGS. 6-8.

In some embodiments, the long-haul all-optical communication path 20 hasa C_(PRE) that is selected to optimally suppress nonlinear signaldistortions over the length of the optical communication path 20.Methods for selecting such an optimal C_(PRE), are, e.g., described inU.S. patent application Ser. No. 10/152,645 ('645), filed by Rene′-JeanEssiambre and Lisa Wickham on May 21, 2002. Said '645 patent applicationis incorporated herein by reference in its entirety.

In some embodiments of the long-haul all-optical, communication path 20with a doubly periodic dispersion map and transmission spans 26 ofPDSMF, the pre-transmission dispersion compensation, C_(PRE), may besuch that C_(PRE)=−NC_(RDPS)/2+(D/α)ln([1−exp(−αL_(span))]/2)±20% orpreferably ±5%. Here, α, D, and L_(span) are the average power loss perunit length in the PDSMFs of the transmission spans 26, the averagedispersion in the PDSMFs of the transmission spans 26, and the averagelength of the PDSMFs of the transmission spans 26 of the path 20,respectively. N is the number of transmission spans 26 in a macro-periodor repeat unit of the doubly periodic map. C_(RDPS) is the residualdispersion per span averaged over the transmission spans 26 of theoptical communication path 20. FIG. 3B illustrates a process 50 foroperating the long haul all-optical communication path 20 of FIG. 3A.The process 50 includes receiving streaming digital optical datasignals, e.g., optical pulses, from optical transmitter 22 (step 52).The process 50 includes optically transporting the streaming digitaloptical data signals over a sequence of transmission spans of theall-optical communication path 20 (step 54). Herein, the expression “asequence of spans” is meant to encompass either a sequence ofconsecutive spans in the associated communication path or a sequence ofnon-consecutive spans of the associated communication path. The sequenceincludes 70 percent or more of the spans of the all-optical long-haulcommunication path 20 and may include 80 percent or more of the spans,90 percent or more of the spans, or even all the spans of the path 20.The transporting step 54 transmits the streaming digital optical data toreceiver 24 at the selected bit rate and wavelength of the transmitter22 via transmission spans 26 of SMF. For the selected wavelength, eachspan 26 has during operation one or more local maximum optical powerpoints on the transmission fiber thereof. For the selected wavelength, aprimary local maximum power point of a given transmission span 26 is thelocal maximum power point located nearest to the signal input in the SMFof the given transmission span 26. The transporting step 54 causescumulative dispersions of the transported optical data signals, e.g.,optical pulses, to evolve along a dispersion map of the path 20. Thedispersion map is such that residual dispersions per span are positiveover some ones of the spans 26 of SMF in the sequence at the selectedwavelength and such that residual dispersions per span are negative overother ones of the spans 26 of SMF in the sequence at the selectedwavelength. For example, the map may be a doubly periodic map or a mapof non-definite periodicity. During operation, each SMF of atransmission span 26 in the sequence has one or more segments (HPS)where a time-averaged optical power at the selected wavelength is atleast 0.2 times the largest value of a time-averaged optical power atthe wavelength along the same SMF. For the selected wavelength, on theprimary one of the above segments, an integral of a time-averagedoptical power along the length thereof is greater than or equal to anintegral of the optical power along any other one of the above segmentsfor the same fiber. In said primary ones of the segments of the fibersin the sequence, magnitudes of cumulative dispersions of the opticaldata signals in pico seconds per nanometer remain less than 32,000 timesthe inverse of the bit rate in giga bits per second.

FIGS. 3C-3E illustrate the above-described high optical power segments(HPSs) and local maximum power points (LMPPs) at the selectedwavelength. The illustrated spans 26 of FIGS. 3C-3E have SMFs of length,L, and use different amplification schemes. The amplification schemesare EDFA, backward Raman, and combined forward and backward Ramanamplification, respectively. In the various cases, the SMF has one ortwo local maximum power points at the selected signal wavelength. Formany amplification schemes, the integral of the signal optical powerover a segment of the path is larger if the segment is near the signalinput of a transmission span than if the segment is near the signaloutput of the span. For example, in FIG. 3D, the optical powerintegrated along the high power segment (HPS-1) near the input of theSMF is larger than the optical power integrated along the other highpower segment (HPS-2) of the same SMF. Thus, nonlinear effects from thehigh power segment (HPS-1) close to the input of the fiber are typicallymore important than such effects from any other high power segment(HPS-2) therein. Therefore, at primary local maximum power points ofSMFs of the sequence of spans 26, magnitudes of cumulative dispersionsof the optical data signals in pico seconds per nanometer are desirablyless than 32,000 times the inverse of the bit rate in giga bits persecond. At the selected wavelength, the primary local maximum powerpoint of a span 26 is the local maximum power point of the associatedSMF that is located nearest the input to the SMF. Preferably, at saidprimary local maximum power points, cumulative dispersions are also lessthan 16,000 times the inverse of the bit rate in giga bits per second.

Herein, for optical pulses, cumulative dispersions are defined by theevolution of pulse widths and for phase modulations of an opticalcarrier, are defined by the evolution of distances between adjacentphase modulations of the carrier.

For some embodiments of the above process, in said segments, cumulativedispersions of the digital optical data signals in pico seconds pernanometer at said points may remain less than about 16,000 times theinverse of the bit rate in giga bits per second. The streaming digitaloptical signals and transporting of said optical signals may be in apseudo-linear transmission regime (PLTR). Since typical embodiments oflong haul, all-optical, communication path 20 incorporate transmissionspans 26 of PDSMF, these optical communication paths 20 can beimplemented as a relatively inexpensive improvement to many deployedlong-haul optical communication paths. In particular, implementing suchan improvement would not typically involve the replacement of alreadydeployed optical transmission spans. Instead, implementation wouldinvolve replacing dispersion compensators, e.g., compensators 30, 34,38. The dispersion compensators are lumped devices, which are morereadily accessed and replaced than deployed optical fiber of longtransmission spans. For that reason, such improvements should be muchless costly than improvements that involve replacing the opticaltransmission spans themselves. Implementing various embodiments ofoptical path 20 as improvements to deployed systems should, e.g., bemuch less costly than replacing deployed transmission spans ofnon-hybrid optical fiber with hybrid optical fibers. Herein, a hybridoptical fiber is an optical fiber that is formed of an alternatingsequence of segments of positive dispersion optical fiber and segmentsof negative dispersion optical fiber.

Recent simulation-based studies account better for intra-channelinteractions between long trains of optical pulses than simulations ofearlier studies. Earlier studies typically simulated well interactionsbetween short random sequences of optical pulses, but did not faithfullysimulate interactions between long pseudo-random sequences of opticalpulses. The recent studies more faithfully simulate interactions betweenlong random sequences of optical pulses. The results of these studiesindicate that dispersion maps with low total excursion have advantagesover maps with large total excursion.

The results of other recent studies indicate that non-singly periodicdispersion maps have advantages over singly periodic dispersion mapshaving comparable total excursions.

Herein, the total excursion is the maximum value in a particular set.The set's members are the magnitude(s) of the difference(s) between thecumulative dispersion at the local maximum optical power point(s) of onespan of transmission fiber and the cumulative dispersion at the localmaximum optical power point(s) of another span of transmission fiber.The set includes value(s) for said magnitude(s) for all pairs ofdifferent spans of the associated optical communication path.

The definition of the one or more local maximum optical power points ofa transmission fiber depends on the amplification scheme for the span.If the optical pulses are optically amplified prior to the transmissionfiber of a span, e.g., via rare-earth amplification or forward Ramanoptical amplification, a single local maximum power point is located ator near the “input” end of the transmission fiber. If the optical pulsesare backward Raman optically amplified along the transmission fiber of aspan, a single local maximum power point is at the “output” end of thetransmission fiber. If the optical pulses are both optically amplifiedprior to the transmission fiber of a span and backward Raman opticallyamplified along the transmission fiber, the transmission fiber has twolocal maximum power points; one is located at the “input” end of thefiber and one is located at the “output” end of the transmission fiber.FIG. 6 illustrates the total excursion for various optical amplificationschemes. In the cases where optical amplification is prior totransmission to each transmission fiber, optical amplification isbackward along each transmission fiber, and optical amplification isboth prior to transmission to each transmission fiber and backward alongeach transmission fiber, the total excursion is given by TE_(p), TE_(B),and TE_(PB), respectively, as shown in FIG. 6.

FIGS. 5A and 5B plot simulated predictions for values of the ROSNR thatare needed to obtain a preselected bit error rate (BER) of 10⁻⁹ at a bitrate of 40 Gb/s. FIG. 5A and FIG. 5B show the ROSNR values obtained foran exemplary optical communication path 20 in a single channel mode andin a dense wavelength-division multiplexed (DWDM) mode, respectively.The simulated values are based on an optical communication path 20 withtwenty-eight identical transmission spans 26, wherein each transmissionspan 20 includes 80 kilometers (km) of standard single mode opticalfiber (SSMF), i.e., PDSMFs. The simulations assumed that each SSMF had adispersion of 17 ps/[(nm)(km)], a dispersion slope of 0.055ps/[(nm²)(km)], a loss coefficient of 0.2 dB/km, and a nonlinearcoefficient γ of 1.22/[(watt)(km)]. The simulations also assumed thatthe optical communication path 20 has a singly periodic dispersion mapin which C_(PRE) has been optimized in terms of C_(RDPS) as alreadydescribed herein. The simulated optical communication path 20 hasin-line amplifiers 28 that operate as EDFAs and that introducenegligible nonlinear optical effects, i.e., due to assumed low powerlevels therein. The simulations used a De Bruijn bit sequence (DBBS) tosimulate pseudo-random intra-channel interactions between sequences ofoptical pulses. The plotted ROSNR values were obtained from DBBSs thatsubstantially reproduce intra-channel inter-pulse interactions forpseudo-random sequences with as many as 11 bits.

FIGS. 5A and 5B show simulated values of the ROSNR for different regimesof C_(RDPS). Herein, the ROSNR is the minimum optical signal to noiseratio that is needed to obtain transmission with no more than apreselected bit error rate. The different values of C_(RDPS) lead todifferent values for the C_(PRE) that optimizes the singly periodic map.The different simulated regimes correspond to values of CRDPs near 50ps/nm, 25 ps/nm, and 10 ps/nm, respectively and are shown by respectivecircular, square, and triangular data points in FIGS. 5A and 5B. In boththe single frequency-channel mode and the DWDM mode, the values for theROSNR are several dB lower for C_(RDPS) values near the lower 25 ps/nmvalues than for the C_(RDPS) values near 50 ps/nm. In the single channelmode, the values for the ROSNR are also about 2 dB lower for the lowerC_(RDPS) values near 10 ps/nm than for the C_(RDPS) values near 25ps/nm. For the singly periodic map, the low C_(PRE) values correspond todispersion maps having low total excursions. Since maps having low totalexcursions need lower ROSNRs, such maps require less optical power toproduce a selected BER.

In embodiments of optical communication path 20 of FIG. 3A, nonlinearoptical effects will also degrade optical pulses in a manner thatdepends on the total excursion. The dependence of such degradation onthe total dispersion may be related to bit rates. High bit rates producefrequency components that undergo large time shifts while propagatingthrough the optical communication path. The large time shifts produceinteractions between long sequences of optical pulses and should growwith the total excursion of the dispersion map. For that reason, therequired optical signal to noise ratios (ROSNR) should probably alsoincrease with the total excursion.

For these reasons, other dispersion maps with low total excursionsshould require lower ROSNR values for desired BERs than dispersion mapswith higher total excursions. In various embodiments with low totalexcursion, the magnitude of the cumulative dispersion is low and below apreselected maximum value at all locally maximum power points oftransmission spans 26 of FIG. 3A. The preselected maximum value for themagnitude of the cumulative dispersion in pico seconds per nanometer ispreferably about 32,000-16,000 times the inverse of the bit rate in gigabits per second or preferably about 16,000 or less times the inverse ofthe bit rate in giga bits per second. For a bit rate of 40 giga bits persecond, this produces a maximum total excursion of about 400 to 800 picoseconds per nanometer.

For dispersion maps having a nonzero C_(RDPS), a low total excursionoften implies that substantial numbers of local maximum optical powerpoints of the spans of transmission fiber have negative cumulativedispersions and substantial numbers of such points will have positivecumulative dispersions. For example, in some embodiments, the mostnegative cumulative dispersion at any local maximum optical power pointof a span of transmission fiber is about equal to negative one times themost positive cumulative dispersion at any such point. For variousembodiments, the map ratio is preferably near one, e.g., the map ratiomay be in the range of about 0.5 to 2.0. Herein, the map ratio isdefined as the sum of positive cumulative dispersion values at localmaximum optical power points to the sum of the magnitudes of thenegative cumulative dispersion values at local maximum power points.

FIGS. 6-8 show exemplary dispersion maps for the optical communicationpath 20 of FIG. 3A in which total excursions are low.

FIG. 6 shows a singly periodic dispersion map that has a low totalexcursion. For a singly periodic map, the total excursion is themagnitude of the sum of the largest cumulative dispersion at a localmaximum optical power point of the last transmission span plus thenegative of the most negative cumulative dispersion at a local maximumpower point of the first transmission span. For many such maps withsuitably low total excursion, the magnitude of the cumulative dispersionat such points should be about 32,000-16,000 or less ps/nm times theinverse of the bit rate in Gb/s. At a bit rate of 40 Gb/s, the magnitudeof the cumulative dispersion at these points is thus, about 800-400ps/nm or less.

FIG. 7 shows a doubly periodic dispersion map that has low totalexcursion, e.g., a map of an embodiment of optical communication path 20of FIG. 3A. In the doubly periodic map, CRDPs's of some transmissionspans take positive values, and C_(RDPS)′S of other transmission spanstake negative values. Also, in such a map, the cumulative dispersionoscillates in a manner that is periodic in the number of spans. Thismacro-oscillation period that defines the periodicity in a doublyperiodic map is equal to a number of transmission spans, wherein thenumber is larger than one and smaller than the total number oftransmission spans in the optical communication path. For many doublyperiodic maps, the total excursion is about equal to the differencebetween the cumulative dispersion at a maximum optical power point in alast transmission span of such a macro-oscillation cycle minus thecumulative dispersion at a maximum optical power point in the firsttransmission span of the same macro-oscillation cycle. In embodimentswith doubly periodic maps of low excursion, the maximum magnitude of thecumulative dispersion at local maximum optical power points oftransmission spans is typically about 32,000-16,000 ps/nm times theinverse of the bit rate in Gb/s and is preferably about 16,000 or lessps/nm times the inverse of the bit rate in Gb/s. For a bit rate of 40Gb/s, the magnitude of the cumulative dispersion at these points isabout 800-400 ps/nm or less.

FIG. 8 shows a dispersion map of non-definite periodicity and low totalexcursion, e.g., a map of another embodiment of optical communicationpath 20 of FIG. 3A. In a dispersion map of non-definite periodicity,C_(RDPS)′S of some transmission spans take positive values, andC_(RDPS)′S of other transmission spans take negative values. Also, insuch maps, the cumulative dispersion oscillates between the variousvalues in a manner that is not periodic over any integral number oftransmission spans smaller than the total number of such spans in theoptical communication path. Often, in such dispersion maps, the sign ofthe C_(RPSD) also varies in a manner that is not periodic with anynumber of transmission spans that is less than the total number oftransmission spans in the optical communication path. In variousembodiments having a map of non-definite periodicity and low excursion,the maximum magnitude of the cumulative dispersion at local maximumoptical power points of transmission spans is typically about32,000-16,000 ps/nm times the inverse of the bit rate in Gb/s and ispreferably about 16,000 ps/nm or less times the inverse of the bit ratein Gb/s. For a bit rate of 40 Gb/s, the magnitude of the cumulativedispersion at these points is about 800-400 ps/nm or less.

Typically, a large cumulative dispersion at local maximum optical powerpoints of a few of the transmission spans should not eliminate theadvantage of low cumulative dispersion for the entire opticalcommunication path. The pulse distortion produced by nonlinear opticaleffects at a few such points might not be large if the path has manytransmission spans. Thus, the embodiments of FIGS. 7 and 8 are intendedto also cover optical communication paths and optical transmissionmethods, wherein cumulative dispersions at only a portion of the localmaximum optical power points of transmission fibers satisfy theabove-described limits. In particular, about 80 percent or more andpreferably about 90 percent or more of a path's transmission fibersshould have local maximum optical power points where the cumulativedispersion is about 32,000-16,000 ps/nm or less times the inverse of thebit rate in Gb/s. More preferably, the 80% or more and preferably 90% ormore of such transmission fibers should be such that the cumulativedispersion at local maximum optical power points therein is less thanabout 16,000 ps/nm times the inverse of the bit rate in Gb/s.

Among the dispersion maps useable in optical communication paths, thesingly periodic map has undesirable properties for long haul paths. Inparticular, the singly periodic map produces a large eye closure penaltyfor transmitted pulses. The eye closure penalty is the ratio of theheight of a transmitted optical pulse's eye to the height of a receivedoptical pulse's eye averaged over an ensemble of such received pulses.Eye closure penalties are typically given in decibels (dB).

FIGS. 9 and 10 show simulated DWDM transmission results for an opticalcommunication path similar to path 20 of FIG. 3A except in the totalnumber of transmission spans. The simulated results of FIG. 9 and FIG.10 correspond to dispersion maps that are singly periodic and doublyperiodic, respectively. The simulations of FIGS. 9 and 10 are based ontransmission parameters: RZ optical pulses, a data rate of 40 Gb/s perchannel, a 33% duty cycle, a 100 giga hertz channel spacing, and 0 dBinput power per channel. The simulations are also based on the systemparameters: a fiber dispersion of 4 ps per nm per km, a dispersion slopeof 0.07 ps/nm² per km, a fiber loss of 0.23 dB per km, an opticalnon-linearity coefficient γ of 1.84 per watt per km, lumped andnoiseless optical amplifiers, span lengths of 100 km, and a receiverhaving a 4^(th) order Bessel filter with an optical bandwidth of 80 GHzand an electrical bandwidth of 30 GHz.

FIGS. 9-10 illustrate eye closure penalties for various values ofC_(RPSD) and C_(PRE). Plates A, B, and C illustrate the eye closurepenalty for path lengths of 1,000 kilometers (km), 2,000 km, and 3,000km, respectively. In the plates A, B, C, the white external regions“ER”, dark boundary lines “BL”, light internal regions “LIR”, and darkinternal regions “DIR” represent approximate eye closure penalties of:more than 6 dB, about 5-6 dB, about 3.5-5 dB, and about 0.5-3.5 dB,respectively.

A comparison of corresponding plates A-C of FIGS. 9 and 10 immediatelyevidences that long communication paths produce a smaller eye closurepenalty if they use a doubly periodic dispersion map rather than thesingly periodic dispersion map. In particular, for the 3,000 km longpath, the doubly periodic path produces LIR regions in the C_(RPSD) andC_(PRE) space where the eye closure penalty is about 3.5-5 dB whereasthe singly periodic map only produces ER regions where the eye closurepenalty is greater than about 6 dB. Similarly, for the 2,000 km longpath, the doubly periodic path produces DIR regions in the C_(RPSD) andC_(PRE) space where the eye closure penalty is about 0.5-3.5 dB whereasthe singly periodic map only produces BL and ER regions where eyeclosure penalty is about 5 dB or larger. On the other hand, for theshorter 1,000 km long communication path and for signal power used here,both the singly and doubly periodic dispersion maps produce the DIRregions in the C_(RPSD) and C_(PRE) space where the eye closure penaltyis relatively small, i.e., in the range of about 0.5-3.5 dB.

The results of FIGS. 5A, 5B evidence that doubly periodic dispersionmaps with a low total excursion have advantages over dispersion mapswith a high total excursion. The results of FIGS. 9 and 10 evidence thatdoubly periodic maps also have advantages over singly periodicdispersion maps with comparably low total excursion for longcommunication paths. In some embodiments of optical communication path20 of FIG. 3A, doubly periodic maps have low total excursions andcommunication paths are long, e.g., total path lengths are more than1,000 km and preferably are about 2,000 km or more. Embodiments ofoptical communication path 20 in which the dispersion map has anon-definite periodicity and a low total excursion may also haveadvantages. Some embodiments with such dispersion maps also have longcommunication paths, e.g., total path lengths of more than 1,000 km andpreferably of about 2,000 km or more.

From the disclosure, drawings, and claims, other embodiments of theinvention will be apparent to those skilled in the art.

1. A process for optically transporting digital data over an all-opticallong-haul communication path, comprising: transporting digital opticaldata signals in a pseudo-linear transmission regime at a selected bitrate and a selected wavelength over a sequence of transmission spansincluding 70 percent or more of the spans of a long-haul all-opticalcommunication path having a doubly periodic dispersion map, each spanbeing configured to have one or more local maximum optical power pointsat the selected wavelength on a transmission fiber thereof, thetransporting causing a cumulative dispersion of each transported opticalsignal to evolve such that residual dispersions per span over some onesof the spans are positive and such that residual dispersions per spanover other ones of the spans are negative; wherein for each span, aprimary local maximum power point at the selected wavelength is the oneof the local maximum power points nearest to a signal input in theassociated one of the fibers; wherein at the primary local maximum powerpoint of each span of the sequence, magnitudes of cumulative dispersionsof the digital optical data signals in pico seconds per nanometer areless than 32,000 times the inverse of the bit rate in giga bits persecond; and pre-transmission dispersion compensating each one of thedigital optical data signals with a precompensation C_(PRE); whereinC_(PRE)=−NC_(RDPS)/2+(D/α)ln([1−exp(−αL_(span))]/2)±20%; α and D beingthe respective average power loss per unit length in the transmissionfibers and the average dispersion in the transmission fibers; C_(RDPS)being an average of the residual dispersion per span over the spans ofthe path; L_(span) being an average length of said transmission fibers;and N being the number of transmission spans in a repeat unit of thedoubly periodic dispersion map.
 2. The process of claim 1, wherein eachtransmission fiber is a non-hybrid optical fiber and each transmissionspan of the sequence includes a dispersion compensator cascaded with thetransmission fiber of the same span.
 3. The process of claim 1, whereinat the primary local maximum power point at the wavelength of each spanof the sequence, cumulative dispersions of the digital optical datasignals in pico seconds per nanometer are less than 16,000 times theinverse of the bit rate in giga bits per second.
 4. The process of claim1, wherein the selected bit rate is 20 giga bits per second or higher;and wherein a portion of the transmission fibers have lengths of 80kilometers or more.
 5. The process of claim 1, wherein the digitaloptical data signals are optical pulses.
 6. The process of claim 5,wherein a combined length of the transmission fibers of the opticalcommunication path is 2,000 kilometers or more.
 7. A long-haulall-optical communication system for transmitting optical pulses at aselected bit rate and a selected wavelength, comprising: a sequence ofspans forming 80 percent of the transmission spans of the all-opticallong-haul optical communication path, each span of the sequenceincluding a positive dispersion transmission optical fiber, an opticalamplifier, and a dispersion compensator; and wherein the path isconfigured to cause cumulative dispersions of the pulses to evolve suchthat residual dispersions per span are positive over some ones of thespans of the sequence and are negative over other ones of the spans ofthe sequence; and wherein the path is configured to produce in eachfiber one or more local maximum optical power points at the wavelength,each fiber having one or more segments where during operation atime-averaged optical power at the wavelength is at least 0.2 times thelargest value along the same fiber for the time-averaged optical powerat the wavelength, a primary one of the segments being such that anintegral of a time-averaged optical power at the wavelength along thelength of the primary one of the segments is greater than or equal to anintegral of the optical power at the wavelength along the length of anyother one of the segments for the same fiber; and wherein the path issuch that in said primary ones of the segments of the fibers of thesequence, magnitudes of cumulative dispersions of the optical pulses inpico seconds per nanometer are less than 32,000 times the inverse of thebit rate in giga bits per second.
 8. The optical communication system ofclaim 7, wherein the path is such that in said primary ones of thesegments of at least 90 percent of the fibers of the path, magnitudes ofcumulative dispersions of the optical pulses in pico seconds pernanometer are less than 16,000 times the inverse of the bit rate in gigabits per second.
 9. The system of claim 7, wherein the dispersion map isone of a doubly periodic map and a map having a non-definiteperiodicity.
 10. The system of claim 8, wherein a combined length of thetransmission optical fibers of the optical communication path is 2,000kilometers or more.